# SymPy | Permutation.rank() in Python

• Last Updated : 27 Aug, 2019

Permutation.rank() : rank() is a sympy Python library function that returns the lexicographic rank of the permutation.

Syntax : sympy.combinatorics.permutations.Permutation.rank()

Return : lexicographic rank of the permutation

Code #1 : rank() Example

 `# Python code explaining``# SymPy.Permutation.rank()`` ` `# importing SymPy libraries``from` `sympy.combinatorics.partitions ``import` `Partition``from` `sympy.combinatorics.permutations ``import` `Permutation`` ` `# Using from sympy.combinatorics.permutations.Permutation.rank() method `` ` `# creating Permutation``a ``=` `Permutation([[``2``, ``0``], [``3``, ``1``]])`` ` `b ``=` `Permutation([``1``, ``3``, ``5``, ``4``, ``2``, ``0``])`` ` ` ` `print` `(``"Permutation a - rank form : "``, a.rank())``print` `(``"Permutation b - rank form : "``, b.rank())`

Output :

Permutation a – rank form : 16
Permutation b – rank form : 191

Code #2 : rank() Example – 2D Permutation

 `# Python code explaining``# SymPy.Permutation.rank()`` ` `# importing SymPy libraries``from` `sympy.combinatorics.partitions ``import` `Partition``from` `sympy.combinatorics.permutations ``import` `Permutation`` ` `# Using from sympy.combinatorics.permutations.Permutation.rank() method `` ` `# creating Permutation``a ``=` `Permutation([[``2``, ``4``, ``0``], ``                 ``[``3``, ``1``, ``2``],``                 ``[``1``, ``5``, ``6``]])`` ` ` ` `print` `(``"Permutation a - rank form : "``, a.rank())`

Output :

Permutation a – rank form : 2461

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